For a series of applications as, e.g., the instrumentally aided repair of surface coatings defects in body shops or recipe calculation in colouristic laboratories base, data have to be generated on a reference system/instrument, to which subsequently all systems/instruments in a distributed network of colour measurement instruments do have access to. The measurement technology utilised in a network can be homogeneous (systems of equal type) or heterogeneous (systems of different type). The latter is probable in applications, where databases have to be maintained across generations of instruments. In such cases the transferability of absolute colour coordinates is a condition precedent to efficiently support the respective process by the associated application. However, various random, systematic, and coarse error sources limit the attainable performance of an application.
For the analysis of random errors efficient statistical tools have been developed and can be utilised to successfully analyse experimental data.
Coarse errors result from carelessness as, e.g., flawed readings of an instrument display. They are not subject to considerations of an error theory, but they can often be identified as so-called outliers in a sample, being markedly different from all other measurement results.
In experiments, systematic errors can occur with certain regularity and can be constant or vary in a predictive fashion. Causes of the systematic errors can be of instrumental or personal origin and may not be easy to detect. Statistical analyses of such systematic errors in general may not be meaningful. Some reproducible systematic errors can be traced back to one or more flawed calibrations or the bias of an observer. These errors have to be estimated by means of a thorough analysis of experimental conditions and techniques. In some cases, where type and extent of errors are known, corrections to experimental data can be performed to compensate systematic errors. For some errors associated with instrument scales such as the photometric scale defined by the instrument calibration, or the wavelength and angle scales defined by the instrument manufacturer, physically motivated correction models have been constructed.
An error model must be generally applicable across all modern instrument configurations and measurement geometries. A fundamental model is required to efficiently correct systematic errors in spectrophotometric measurements associated with all instrument scales: photometric scale, wavelength scale, and angle scale. Sound physical models can be derived leading to spectral differences between instruments, which can be used to predict systematic errors.
However, physically meaningful error models have been introduced, for example, by Robertson to correct photometric and wavelength scales only (A. R. Robertson, Diagnostic performance evaluation of spectrophotometers, in Advances in Standards and Metrology in Spectrophotometry, ed. by C. Burgess and K. D. Mielenz, p. 277, Elsevier Science Publishers B. V., Amsterdam (1987)). These models have been generalised and extended to improve their performance and efficiency. Models for correcting errors of the angle scale of goniospectrophotometers have not been published so far.
In practical applications differences in geometrical measurement conditions may occur, where colour measurement instruments are slightly tilted by the operator during the measurement process, or where those instruments are mounted in a measurement robot used in an application where contact-free measurements have to be carried out. In both cases tilted measurement plane will have the biggest impact on readings of angles close to the specular. Typically this is an angle as close as 15° to the gloss angle. When measuring brilliant metallic colour shades a misalignment of the measurement plane of only 0.1° might be sufficient to give rise to an out-of-specification situation.